I'm still on the trail of the new word nother. Recently my sister said, 'That'll weigh a good nother kilo, I reckon'.
Okay... now I've heard a different word than whole inserted between an and other.
So now I think maybe our brains are processing the expression as one word rather than as a phrase. Maybe it's the word another with an infix in it.
When I looked up infix in the Merriam Webster online, I was surprised to discover it can be a transitive verb or an adjective as well as a noun. However, it seems as if we don't use infixes much in English compared to other languages.